The kindling were used (in conjunction with a tinderbox) to start a fire around one side of an evil tree. Multiple fires could have been created to completely surround the tree, slightly adding to the damage inflicted.

However, burning kindling had no quest significance whatsoever; it was completely optional, and players would've still received a Year even if they had not lit any fires to the tree (but you had to have chopped at the tree at least once).